Using a predetermined ablation-current profile

ABSTRACT

Described embodiments include a system that includes a current source generator and a processor. The processor is configured to drive the current source generator to supply, for application to tissue of a subject, an electric current having an amplitude that varies in accordance with a predefined function of time, such that the amplitude initially monotonically increases to a maximum value. Other embodiments are also described.

FIELD OF THE INVENTION

The present invention is related to the field of medical devices andtreatments, particularly those associated with the ablation ofbiological tissue.

BACKGROUND

During some types of ablation procedures, an ablation electrode isbrought into contact with the tissue that is to be ablated, and electriccurrents are then passed through the tissue, causing a lesion to beformed in the tissue.

U.S. Pat. No. 5,735,846 describes systems and methods for ablating bodytissue. An electrode contacts tissue at a tissue-electrode interface totransmit ablation energy at a determinable power level. The systems andmethods include an element to remove heat from the electrode at adeterminable rate. The systems and methods employ a processing elementto derive a prediction of the maximum tissue temperature conditionoccurring beneath the tissue-electrode interface. The processing elementcontrols the power level of ablation energy transmitted by theelectrode, or the rate at which the electrode is cooled, or both, based,at least in part, upon the maximum tissue temperature prediction.

U.S. Pat. No. 9,241,756 to Berger et al., whose disclosure isincorporated herein by reference, describes a method for performing amedical procedure, which includes coupling a probe to tissue in an organof a patient. Ablation energy is applied to the tissue using the probe.A model of an evolution of steam pressure in the tissue, caused by theablation energy, as a function of time is estimated. Based on the model,an occurrence time of a steam pop event caused by the steam pressure ispredicted, and the predicted occurrence time of the steam pop event isindicated to an operator.

U.S. Pat. No. 9,265,574 to Bar-tal et al., whose disclosure isincorporated herein by reference, describes apparatus, consisting of aprobe, configured to be inserted into a body cavity, and an electrodehaving an outer surface and an inner surface connected to the probe. Theapparatus also includes a temperature sensor, protruding from the outersurface of the electrode, which is configured to measure a temperatureof the body cavity.

Mudit K. Jain and Patrick D. Wolf, “A three-dimensional finite elementmodel of radiofrequency ablation with blood flow and its experimentalvalidation,” Annals of Biomedical Engineering 28.9 (2000): 1075-1084,describes a three-dimensional finite element model for the study ofradiofrequency ablation. The model was used to perform an analysis ofthe temperature distribution in a tissue block heated by RF energy andcooled by blood (fluid) flow. The effect of fluid flow on thetemperature distribution, the lesion dimensions, and the ablationefficiency was studied.

SUMMARY OF THE INVENTION

There is provided, in accordance with some embodiments of the presentinvention, a system that includes a current source generator and aprocessor. The processor is configured to drive the current sourcegenerator to supply, for application to tissue of a subject, an electriccurrent having an amplitude that varies in accordance with a predefinedfunction of time, such that the amplitude initially monotonicallyincreases to a maximum value.

In some embodiments, the predefined function of time includes a timeseries of values.

In some embodiments, the predefined function of time returns, for anyvalue of time t, (a+t^(b))/(c+d*t^(e)+f*t^(g)) for constants a, b, c, d,e, f, and g.

In some embodiments, the amplitude is a root mean square (RMS)amplitude, and the maximum value of the RMS amplitude is between 0.8 and1.2 A.

In some embodiments, the processor is configured to cause the amplitudeto monotonically increase to the maximum value in less than 0.5 s.

In some embodiments, the processor is further configured to:

during the application of the electric current and following theincrease of the amplitude to the maximum value, receive a signalindicating a surface temperature of the tissue, and

in response to the signal, adjust the amplitude of the electric current.

In some embodiments, the processor is further configured to calculate anestimated maximum subsurface temperature of the tissue from the surfacetemperature, and the processor is configured to adjust the amplitude ofthe electric current responsively to the estimated maximum subsurfacetemperature.

In some embodiments, the electric current is applied to the tissue by adistal tip of a catheter, and the processor is further configured to:

calculate an estimated depth of penetration into the tissue of thedistal tip of a catheter, and

select the predefined function of time from multiple predefinedfunctions of time, responsively to the estimated depth of penetration.

There is further provided, in accordance with some embodiments of thepresent invention, a method that includes loading, from a computermemory, a predefined function of time, and driving a current sourcegenerator to supply, for application to tissue of a subject, an electriccurrent having an amplitude that varies in accordance with thepredefined function of time, such that the amplitude initiallymonotonically increases to a maximum value.

There is further provided, in accordance with some embodiments of thepresent invention, a system that includes a computer memory and aprocessor. The processor is configured to, while simulating anapplication of an electric current to simulated tissue, control anamplitude of the electric current such that a maximum subsurfacetemperature of the simulated tissue increases toward a predefinedthreshold without exceeding the predefined threshold. The processor isfurther configured to derive a function of time from values of theamplitude over the simulated application, and to store the function oftime in the computer memory for subsequent use in an ablation procedure.

In some embodiments, the processor is configured to, by controlling theamplitude, cause the amplitude to initially monotonically increase to amaximum value.

In some embodiments, the amplitude is a root mean square (RMS)amplitude, and the maximum value of the RMS amplitude is between 0.8 and1.2 A.

In some embodiments, the processor is configured to cause the amplitudeto monotonically increase to the maximum value in less than 0.5 s.

In some embodiments, the processor is configured to, by controlling theamplitude, cause the maximum subsurface temperature to increase towithin 5° C. of the predefined threshold in less than 1.5 s from a startof the simulated application, and to then remain within 5° C. of thepredefined threshold until an end of the simulated application.

In some embodiments, the processor is configured to derive the functionof time by selecting at least some of the values of the amplitude overthe simulated application, and to store the function of time by storingthe selected values.

In some embodiments, the processor is configured to derive the functionof time by fitting a predefined function template to the values of theamplitude over the simulated application.

In some embodiments, the function of time returns, for any value of timet, (a+t^(b))/(c+d*t^(e)+f*t^(g)) for constants a, b, c, d, e, f, and g.

In some embodiments, the processor is configured to control theamplitude by, given a current amplitude-value A of the amplitude and acurrent temperature-value T of the maximum subsurface temperature,setting a next value of the amplitude to min(A, max(A_(min),|A_(min)−C*(T−T_(lim))|)), where A_(min) is a predefined minimumamplitude value, C is a predefined constant, and T_(lim) is thepredefined threshold.

In some embodiments, the processor is configured to cause the maximumsubsurface temperature to increase asymptotically toward the predefinedthreshold by controlling the amplitude.

In some embodiments,

the electric current is a simulated electric current,

the amplitude is a simulated amplitude,

the system further includes a current source generator, and

the processor is further configured to drive the current sourcegenerator to supply an actual electric current having an actualamplitude that varies in accordance with the function of time during theablation procedure.

In some embodiments, the predefined threshold is between 120 and 130° C.

There is further provided, in accordance with some embodiments of thepresent invention, a method that includes, using a processor, whilesimulating an application of an electric current to simulated tissue,controlling an amplitude of the electric current such that a maximumsubsurface temperature of the simulated tissue increases toward apredefined threshold without exceeding the predefined threshold. Themethod further includes deriving a function of time from values of theamplitude over the simulated application, and storing the function oftime for subsequent use in an ablation procedure.

The present invention will be more fully understood from the followingdetailed description of embodiments thereof, taken together with thedrawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a system for ablating tissue of asubject, in accordance with some embodiments of the present invention;

FIG. 2 is a schematic illustration of two electric-current profiles, inaccordance with some embodiments of the present invention; and

FIG. 3 is a schematic illustration of a simulated ablation used togenerate an electric-current profile, in accordance with someembodiments of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS Overview

In general, it is desirable that an ablation procedure proceed asquickly as possible. However, applying a large amount of power to thetissue within a short interval of time may cause the subsurfacetemperature of the tissue to become too high, such that dangerous steampops may form within the tissue. One solution is to estimate thesubsurface temperature during the procedure, as described, for example,in the aforementioned U.S. Pat. Nos. 9,241,756 and 9,265,574. However,in some cases, this solution may be difficult to implement effectively.

To address this challenge, embodiments of the present invention utilize,for the procedure, a predetermined ablation-current profile that isknown to safely deliver a large amount of power within a small intervalof time. To generate the profile, a processor simulates the effect of anablation current on the subsurface temperature of the tissue. Inparticular, the processor computes a time-varying current amplitude thatcauses the maximum subsurface temperature of the tissue to quicklyapproach a maximum allowable temperature value T_(lim), and thencontinue to approach T_(lim), or at least remain near T_(lim), withoutexceeding T_(lim).

Subsequently, during the procedure, the processor drives a generator togenerate an ablation current in accordance with the profile.

In each ablation-current profile, the amplitude of the current initiallyincreases rapidly to a relatively large maximum value. This initialburst of current causes the maximum subsurface temperature to quicklyapproach T_(lim), as described above. Subsequently, after an optionalplateau at the maximum value, the amplitude decreases measuredly fromthe maximum value, such that the maximum subsurface temperature does notexceed T_(lim).

In general, during an ablation procedure, the temperature of the tissueincreases as a function of the density of the current that is applied tothe tissue. Hence, embodiments described herein typically use a currentsource generator, such that the applied current density does not varywith any changes in the impedance of the tissue that may occur as thetissue is heated. In contrast, were a power source generator used, theapplied current density might vary with changes in the tissue impedance,leading to unexpected changes in the temperature of the tissue.

System Description

Reference is initially made to FIG. 1, which is a schematic illustrationof a system 20 for ablating tissue of a subject 26, in accordance withsome embodiments of the present invention.

FIG. 1 depicts a physician 28 performing an ablation procedure onsubject 26, using an ablation catheter 22. In this procedure, physician28 first inserts the distal tip 40 of catheter 22 into the subject, andthen navigates distal tip 40 to the tissue that is to be ablated. Forexample, the physician may advance the distal tip through thevasculature of the subject until the distal tip is in contact withtissue located within the heart 24 of the subject. Next, the physicianinstructs a processor 36 to apply an electric current to the tissue. Inresponse to this instruction, processor 36 loads a predeterminedelectric-current profile, which specifies an electric-current amplitudeas a function of time, from a computer memory 32. Processor 36 thendrives a current source generator 30 to supply an electric currenthaving an amplitude that varies in accordance with the function of time.The electric current runs through catheter 22 to distal tip 40, and thenpasses through the tissue that contacts distal tip 40. For example, in aunipolar ablation procedure, the electric current may pass between oneor more electrodes on distal tip 40 and a neutral electrode patch 31that is coupled externally to the subject, e.g., to the subject's back.

Typically, catheter 22 is connected to a console 34, which containsprocessor 36, memory 32, and generator 30. Console 34 comprises a userinterface, comprising, for example, a keyboard, a mouse, and/orspecialized controls 35, which may be used by physician 28 to provideinput to processor 36. Alternatively or additionally, during theprocedure, physician 28 may use a foot pedal to issue instructions toprocessor 36. In some embodiments, system 20 further comprises a display38, and processor 36 causes display 38 to display relevant output tophysician 28 during the procedure.

Processor 36 may be connected to memory 32 over any suitable wired orwireless interface, over which the processor may store information to,or retrieve information from, the memory. Such information may include,for example, specifications for an electric-current profile, describedbelow with reference to FIG. 2. Memory 32 may comprise any suitable typeof computer memory, such as, for example, a hard drive or flash drive.

Similarly, processor 36 may be connected to generator 30 over anysuitable wired or wireless interface, over which the processor maycommunicate instructions to generator 30, e.g., such as to cause thegenerator to generate an electric current that tracks a predefinedelectric-current profile.

Typically, multiple profiles, for different respective sets of ablationparameters, are stored in memory 32. Prior to the application of theelectric current to the tissue of the subject, the processor receives orcalculates the relevant parameters, and then selects, from the multipleprofiles, the profile that corresponds to these parameters.

One such parameter is the thickness of the tissue. In general, forthicker tissue, less current is required to attain a given increase intemperature, relative to thinner tissue. In some embodiments, anestimation of this parameter is input manually by a user. Alternatively,an ultrasound transducer within distal tip 40 may acquire an ultrasoundimage of the tissue, and the processor may then ascertain the thicknessof the tissue from the image, as described, for example, in US2018/0008229, whose disclosure is incorporated herein by reference.

Another relevant parameter is the flow rate of the irrigation fluid thatis passed from the distal tip. In general, as the flow rate increases,more heat is evacuated from the tissue, such that more current isrequired to achieve a given increase in temperature.

Other relevant parameters include the force with which distal tip 40contacts the tissue, and the penetration depth of the distal tip, whichdepends on this force. (In the context of the present application,including the claims, the catheter tip is said to “penetrate” the tissueif the catheter tip presses the surface of the tissue inward. Thedistance by which the surface is pressed inward is referred to as thepenetration distance or penetration depth.) In general, as thepenetration depth increases, a greater proportion of the ablationcurrent passes through the tissue rather than through the blood, suchthat less current is required to achieve a given increase intemperature.

In some embodiments, a force sensor at distal tip 40 measures thecontact force, and the processor then calculates an estimatedpenetration depth of distal tip 40 responsively to this forcemeasurement. Alternatively or additionally, a temperature sensor atdistal tip 40 may measure the temperature at the distal tip, and theprocessor may then calculate the penetration depth responsively to thistemperature measurement. Alternatively or additionally, an impedance maybe measured between the distal tip and a reference electrode that iscoupled externally to the subject, and the processor may then calculatethe penetration depth responsively to this impedance measurement.

For example, to estimate the penetration depth, the processor may useany of the techniques described in U.S. Pat. No. 9,241,756 to Berger etal. and U.S. Pat. No. 9,265,574 to Bar-tal et al., whose respectivedisclosures are incorporated herein by reference. Per one suchtechnique, the processor first estimates the penetration depth of thedistal tip using the aforementioned impedance and force measurements,and then re-estimates this depth until a match is found between thesemeasurements and the temperature and impedance values calculated by afinite element model.

In general, processor 36 may be embodied as a single processor, or as acooperatively networked or clustered set of processors. In someembodiments, the functionality of processor 36, as described herein, isimplemented solely in hardware, e.g., using one or moreApplication-Specific Integrated Circuits (ASICs) or Field-ProgrammableGate Arrays (FPGAs). In other embodiments, the functionality ofprocessor 36 is implemented at least partly in software. For example, insome embodiments, processor 36 is embodied as a programmed digitalcomputing device comprising a central processing unit (CPU), randomaccess memory (RAM), non-volatile secondary storage, such as a harddrive or CD ROM drive, network interfaces, and/or peripheral devices.Program code, including software programs, and/or data are loaded intothe RAM for execution and processing by the CPU and results aregenerated for display, output, transmittal, or storage, as is known inthe art. The program code and/or data may be downloaded to the processorin electronic form, over a network, for example, or it may,alternatively or additionally, be provided and/or stored onnon-transitory tangible media, such as magnetic, optical, or electronicmemory. Such program code and/or data, when provided to the processor,produce a machine or special-purpose computer, configured to perform thetasks described herein.

Using an Electric-Current Profile

Reference is now made to FIG. 2, which is a schematic illustration oftwo electric-current profiles 42, in accordance with some embodiments ofthe present invention.

By way of example, FIG. 2 shows two profiles 42 that were generatedusing the simulation techniques described below with reference to FIG.3: a first profile 42 a, corresponding to a penetration depth of 0.25 mmand a tissue thickness of approximately 4 mm, and a second profile 42 b,corresponding to a penetration depth of 0.55 mm and a tissue thicknessof approximately 4 mm. As noted above, by controlling the current sourcegenerator, the processor may cause the electric current that isgenerated by the generator and applied to the subject to track eitherone of these profiles.

Since the currents used for ablation are typically alternating currents(e.g., at radiofrequencies), FIG. 2 plots the root mean square (RMS)amplitude of the currents, and portions of the description belowsimilarly refer to the RMS amplitude, per the convention in the art. Itis noted, however, that a current profile may alternatively be definedin terms of the peak amplitude of the current, or any other suitablemeasure of amplitude.

As shown in FIG. 2, the RMS amplitude of the current initiallyincreases, typically (but not necessarily) monotonically, to arelatively high maximum value A_(max), which is, for example, between0.8 and 1.2 A. Typically, this initial increase in amplitude is as rapidas generator 30 allows; thus, for example, the amplitude may increase toA_(max) in less than 0.5 s. Subsequently, the amplitude remains at orbelow A_(max) until the end of the application of the current. Forexample, the amplitude may plateau at A_(max) (or at least remain withinless than 1% of A_(max)) for a particular interval of time, beforedecreasing over time (with the possible exception of one or more smallintermittent increases), such that the amplitude remains below themaximum value until the end of the application of the current.

For example, following the plateau at A_(max), the amplitude maydecrease to a lower value A₀ that is between 50% and 70% of A_(max), andthen remain relatively constant over the “tail” portion of the profile,such that, for example, the amplitude remains within ±10% of A₀. Ingeneral, a deeper penetration of the distal tip of the catheterfacilitates greater efficiency in heating the tissue. Hence, theamplitude A₀ generally decreases with increase of the penetration depth,as can be observed by comparing first profile 42 a to second profile 42b.

Advantageously, during the application of the electric current, it maynot be necessary to receive or process any information from the distaltip of the catheter. Rather, the generated electric current may simplytrack the predefined profile until the physician instructs theprocessor, at any suitable moment in time, to terminate the applicationof current, as indicated in FIG. 2 by an “END” indicator. In general,the physician may set the duration of the application of current inaccordance with the desired width and/or depth of the lesion, as furtherdescribed below with reference to FIG. 3. Alternatively, the generatedelectric current may track the predefined profile for a predeterminedinterval of time. Such an interval may have a duration of, for example,between 3 and 30 s, such as between 10 and 20 s.

Notwithstanding the above, in some embodiments, the processor maydeviate from the predefined profile, in response to feedback receivedduring the procedure. For example, during the application of theelectric current and following the increase of the amplitude to themaximum value, the processor may receive one or more signals thatindicate a surface temperature of the tissue. (Such signals may bereceived, for example, from one or more temperature sensors, such asthermocouples, disposed at distal tip 40.) In response to these signals,the processor may adjust the amplitude of the electric current, e.g., byadjusting the amplitude of the tail of the profile, as indicated in FIG.2 by a double-sided arrow 44. For example, in response to receiving asurface temperature reading that is higher than expected, the processormay lower the amplitude of the current, to avoid overheating the tissue.Conversely, in response to receiving a surface temperature reading thatis lower than expected, the processor may raise the amplitude of thecurrent.

In some embodiments, the processor calculates an estimated maximumsubsurface temperature of the tissue from the surface temperature, andadjusts the amplitude of the electric current responsively to theestimated maximum subsurface temperature. For example, if theelectric-current profile is configured to maintain the maximumsubsurface temperature below 120° C., but the processor calculates amaximum subsurface temperature that is greater than 120° C., theprocessor may reduce the amplitude of the electric current to below theamplitude that is dictated by the electric-current profile.

To estimate the maximum subsurface temperature, the processor may useany of the techniques described in U.S. Pat. No. 9,241,756 to Berger etal. and U.S. Pat. No. 9,265,574 to Bar-tal et al., whose respectivedisclosures are incorporated herein by reference. For example, theprocessor may evaluate a finite element heat transfer model of thecatheter and tissue environment. The boundary conditions for the modelmay include the measured surface temperature, the estimated tippenetration depth, and the amplitude of the ablation current. Theprocessor may further incorporate the influence of irrigation by settinga convection boundary condition, using, for example, a computationalfluid dynamic (CFD) model.

Generating an Electric-Current Profile

Reference is now made to FIG. 3, which is a schematic illustration of asimulated ablation used to generate an electric-current profile, inaccordance with some embodiments of the present invention.

Typically, processor 36 generates each profile 42 by simulating anablation, i.e., by simulating the application of an electric current tosimulated tissue 46. Such a simulated ablation is depicted pictoriallyin FIG. 3, whereby a simulated catheter tip 40 s applies an electriccurrent to simulated tissue 46 while penetrating the simulated tissue.The various hatch marks beneath the surface 48 of the tissue indicatedifferent respective subsurface temperature ranges, whereby thetemperature is highest within a “hot spot” 47, and is progressivelylower with distance from hot spot 47. The illustration in FIG. 3 isbased on a screenshot of a simulation performed using the Multiphysics®software by COMSOL, Inc. of Burlington, Mass., USA. This software, orany other similar software that models the effect of electric current onbiological tissue, may be used to perform the simulations describedherein.

While simulating the application of the electric current, the processormonitors the maximum subsurface temperature (“maxtemp”) of the simulatedtissue (attained within hot spot 47), and controls the amplitude of theelectric current responsively thereto, as further described below.Following the simulated ablation, the processor derives a function oftime—referred to above as an electric-current profile—from the values ofthe amplitude over the simulated ablation, and then stores the functionof time in memory 32 (FIG. 1) for subsequent use in an ablationprocedure, as described above with reference to FIG. 2.

For example, the processor may select at least some of the values of theamplitude over the simulated application, and then store the selectedvalues. In this case, the stored profile includes a time series ofamplitude values, i.e., multiple values of the amplitude for differentrespective times. Alternatively, the processor may fit a predefinedfunction template to the amplitude values, and then store the resultingfunction. In some embodiments, this template is of the form(a+t^(b))/(c+d*t^(e)+f*t^(g)) for time t and constants a, b, c, d, e, f,and g. In this case, further to fitting the template to the amplitudevalues, the processor stores the constants a through g. (As a purelyillustrative example, in one case, the inventors obtained a=323.2,b=7.345, c=315.3, d=1.299, e=7.432, f=0.1815, and g=−4.729.)

While simulating the ablation, the processor controls the amplitude ofthe simulated current such that the maximum subsurface temperatureincreases toward a predefined temperature threshold (or “limit”) T_(lim)(which is 120° C. in FIG. 3), without exceeding the predefinedthreshold. In particular, the processor may cause the maximum subsurfacetemperature to quickly (e.g., in less than 1.5 s from the start of thesimulated application) increase to within a small margin (e.g., towithin 5° C.) of the predefined threshold, and to then remain withinthis margin until the end of the simulated application. For example,after increasing to within ° C. of the threshold, the maximum subsurfacetemperature may continue increasing, e.g., asymptotically, toward thethreshold.

Typically, the threshold temperature T_(lim) is between 120 and 130° C.In general, T_(lim) is selected to be as high as possible, provided thatthere exist a margin of safety with respect to the critical temperatureat which the probability of a steam pop forming exceeds a giventhreshold. (This temperature is described in the aforementioned U.S.Pat. No. 9,241,756 to Berger et al., whose disclosure is incorporatedherein by reference.) Thus, for example, if the critical temperature is125° C., T_(lim) may be 120° C.; as another example, if the criticaltemperature is 140° C.,

Tli_(m) may be 130° C.

Typically, to cause the maximum subsurface temperature to vary in themanner described above, the processor varies the amplitude of thesimulated current in the manner described above with reference to FIG.2. That is, the processor causes the amplitude to increase rapidly(e.g., in less than 0.5 s) to a maximum value A_(max), and then remainat or below A_(max) until the end of the simulated ablation. Morespecifically, following the initial increase of the amplitude toA_(max), the processor uses a suitable control function to control theamplitude of the simulated current based on the current maximumsubsurface temperature “T.” Such a control function may, for example,set the next value of the amplitude as a function of the differencebetween T and T_(lim), such that, as T approaches T_(lim), the amplitudedecreases. For example, given a current value “A” of the amplitude, thenext value of the amplitude may be set to min (A, max (A_(min),|A_(min)−C*(T−T_(lim))|)), where A_(min) is a predefined minimumamplitude value and C is a predefined constant. (As a purelyillustrative example, A_(min) may be 0.4 A for the RMS amplitude, and/orC may be 0.05.)

Typically, prior to the simulated ablation, the processor receives themaximum amplitude A_(max) and the threshold temperature T_(lim) asinputs. In other embodiments, the processor does not receive a specificA_(max) value as an input. Rather, the processor receives a suitablerange of values for A_(max) (e.g., 0.8-1.2 A for the RMS amplitude).Subsequently, the processor iteratively selects various A_(max) valuesfrom within this range, until a suitable profile is obtained. (It isnoted that, typically, there is no specific “optimal” A_(max), since oneprofile having a larger A_(max) than another profile will also have ashorter plateau at A_(max), such that the two profiles will generallyhave approximately the same effect on the subsurface temperature of thetissue.)

By way of example, FIG. 3 also shows a first plot 50 of the maximumsubsurface temperature over the course of the simulation, in which themaximum subsurface temperature may be seen to increase asymptoticallytoward the predefined threshold of 120° C. FIG. 3 also shows a secondplot 52 of the width of the simulated lesion (in mm) over the course ofthe simulation, along with a third plot 54 of the depth (in mm) of thesimulated lesion. The processor may display these plots to physician 28(FIG. 1) prior to the actual ablation procedure, so that the physicianmay ascertain the duration that corresponds to a particular targetlesion size. The physician may then apply the ablating current for thisduration, such as to achieve the target lesion size. Alternatively, thephysician may input the target lesion depth and/or width, and theprocessor may then apply the ablating current for the duration thatachieves the desired target.

FIG. 3 further includes a fourth plot 56 of the surface temperature oftissue 46—i.e., the temperature of the tissue at surface 48—during thesimulation. Fourth plot 56 demonstrates that the surface temperature maynot be a good indicator for the maximum subsurface temperature.

Typically, the processor performs a different respective set ofsimulations for each type of ablation catheter. That is, for each typeof catheter, the processor performs multiple simulations for varioussets of ablation parameters. As described above with reference to FIG.1, these parameters may include the tissue thickness, contact force,irrigation-fluid flow rate, and/or penetration depth.

In some embodiments, profiles 42 are generated by another processor,rather than by processor 36. Each profile may be stored in any suitablememory, which may be remote from processor 36, prior to beingtransferred to memory 32. (Alternatively, processor 36 may load theprofile directly from the remote memory over any suitable communicationinterface.) Subsequently, during the ablation procedure, the processordrives current source generator 30 (FIG. 1) to supply an electriccurrent having an amplitude that varies in accordance with the profile,as described above with reference to FIG. 2.

It will be appreciated by persons skilled in the art that the presentinvention is not limited to what has been particularly shown anddescribed hereinabove. Rather, the scope of embodiments of the presentinvention includes both combinations and subcombinations of the variousfeatures described hereinabove, as well as variations and modificationsthereof that are not in the prior art, which would occur to personsskilled in the art upon reading the foregoing description. Documentsincorporated by reference in the present patent application are to beconsidered an integral part of the application except that to the extentany terms are defined in these incorporated documents in a manner thatconflicts with the definitions made explicitly or implicitly in thepresent specification, only the definitions in the present specificationshould be considered.

1. A system, comprising: a current source generator; and a processor,configured to drive the current source generator to supply, forapplication to tissue of a subject, an electric current having anamplitude that varies in accordance with a predefined function of time,such that the amplitude initially monotonically increases to a maximumvalue.
 2. The system according to claim 1, wherein the predefinedfunction of time includes a time series of values.
 3. The systemaccording to claim 1, wherein the predefined function of time returns,for any value of time t, (a+t^(b))/(c+d*t^(e)+f*t^(g)) for constants a,b, c, d, e, f, and g.
 4. The system according to claim 1, wherein theamplitude is a root mean square (RMS) amplitude, and wherein the maximumvalue of the RMS amplitude is between 0.8 and 1.2 A.
 5. The systemaccording to claim 1, wherein the processor is configured to cause theamplitude to monotonically increase to the maximum value in less than0.5 s.
 6. The system according to claim 1, wherein the processor isfurther configured to: during the application of the electric currentand following the increase of the amplitude to the maximum value,receive a signal indicating a surface temperature of the tissue, and inresponse to the signal, adjust the amplitude of the electric current. 7.The system according to claim 6, wherein the processor is furtherconfigured to calculate an estimated maximum subsurface temperature ofthe tissue from the surface temperature, and wherein the processor isconfigured to adjust the amplitude of the electric current responsivelyto the estimated maximum subsurface temperature.
 8. The system accordingto claim 1, wherein the electric current is applied to the tissue by adistal tip of a catheter, and wherein the processor is furtherconfigured to: calculate an estimated depth of penetration into thetissue of the distal tip of a catheter, and select the predefinedfunction of time from multiple predefined functions of time,responsively to the estimated depth of penetration.
 9. A method,comprising: loading, from a computer memory, a predefined function oftime; and driving a current source generator to supply, for applicationto tissue of a subject, an electric current having an amplitude thatvaries in accordance with the predefined function of time, such that theamplitude initially monotonically increases to a maximum value.
 10. Themethod according to claim 9, wherein the predefined function of timeincludes a time series of values.
 11. The method according to claim 9,wherein the predefined function of time returns, for any value of timet, (a+t^(b))/(c+d*t^(e)+f*t^(g)) for constants a, b, c, d, e, f, and g.12. The method according to claim 9, wherein the amplitude is a rootmean square (RMS) amplitude, and wherein the maximum value of the RMSamplitude is between 0.8 and 1.2 A.
 13. The method according to claim 9,wherein the amplitude of the electric current monotonically increases tothe maximum value in less than 0.5 s.
 14. The method according to claim9, further comprising: during the application of the electric currentand following the increase of the amplitude to the maximum value,receiving a signal indicating a surface temperature of the tissue; andin response to the signal, adjusting the amplitude of the electriccurrent.
 15. The method according to claim 14, further comprisingcalculating an estimated maximum subsurface temperature of the tissuefrom the surface temperature, wherein adjusting the amplitude of theelectric current comprises adjusting the amplitude of the electriccurrent responsively to the estimated maximum subsurface temperature.16. The method according to claim 9, wherein the electric current isapplied to the tissue by a distal tip of a catheter, and wherein themethod further comprises: calculating an estimated depth of penetrationinto the tissue of the distal tip of a catheter; and selecting thepredefined function of time from multiple predefined functions of time,responsively to the estimated depth of penetration. 17.-40. (canceled)